Question

The sum of two numbers is 35, The smaller number is 21 less than the larger number. What are the numbers?Larger number:Smaller number:

Answer 1

Let x and y be the numbers, such that x is the smaller number. Thus;

`\begin{gathered} x+y=35.........equation1 \\ \\ y=x+21...........equation2 \end{gathered}`

Substitute equation 2 in equation 1;

`\begin{gathered} x+x+21=35 \\ \text{ collect like terms;} \\ 2x=35-21 \\ \\ 2x=14 \\ \text{ Divide both sides by 2;} \\ \\ (2x)/(2)=(14)/(2) \\ \\ x=7 \end{gathered}`

Substitute the value of x in equation 2;

`\begin{gathered} y=7+21 \\ \\ y=28 \end{gathered}`

ANSWERS:

Larger number: 28

Smaller number: 7